Congressional negotiators raced Saturday to write a compromise fiscal package that would limit the effect of tax increases due to take effect Jan. 1 while pushing many important decisions about the federal budget into the new year.

After a full day in which staffers sent papers back and forth, Senate Minority Leader Mitch McConnell of Kentucky left the Capitol shortly before 7 p.m. Saturday, telling reporters the two sides continue to try and reach a deal to avert the fiscal cliff.

“We’ve been trading paper all day and talks continue,” McConnell said. “We’ll let you know as soon as we have some news to make.”

But the talks clearly were in a new, urgent phase, with leadership staff expected to remain in the Capitol as long as necessary “to get where they need to be,” according to one person familiar with the negotiations.

“This is real,” not just for show, the source said.

GOP aides said they don’t expect to have more to say until after lawmakers are briefed Sunday afternoon.

The White House, meanwhile, remained in contact with negotiators and the president was kept informed of the status of the talks.

After weeks spent trying to forge a comprehensive agreement that would settle the long-standing policy challenges under the fiscal cliff, political leaders narrowed their focus almost exclusively to the historically large tax increase that is set to become law when the clock strikes midnight on Monday. Hoping to beat that deadline, the House and Senate will be in session Sunday, when a deal could be presented to rank-and-file members and the following day when legislation could go to the White House for President Barack Obama’s signature in the hours before taxes are set to shift.

If a deal is reached, the Senate could vote on it as early as Sunday.

After a flurry of activity in recent days, the outlines of a potential agreement have come into view. But assembling all the component parts of a package that can win the support of House Republicans and Senate Democrats presented big challenges in such a short time frame.

According to congressional aides, a compromise bill would raise taxes on high-income households, but not by as much as Democrats have wanted. It also would likely continue federal benefits to the long-term unemployed and prevent a reduction in payments to doctors who treat Medicare patients. But it probably would not avert deep automatic cuts to military and nondefense discretionary programs, known as the sequester, or raise the federal debt ceiling. With spending unresolved and the government due to exceed its borrowing authority in the coming week, it’s certain the debate over government spending will consume the first few weeks or months of the next Congress.

If those steps are not taken, and with the government due to exceed its borrowing authority soon, the debate over government expenditures will almost certainly consume the first few weeks or months of the next Congress.

Still unknown is exactly which households would see a tax increase under a Senate agreement. After insisting that rates go up on income above $200,000 for individuals and $250,000 for couples, Democratic leaders have quietly signaled they could push that threshold to $400,000. Although that small change represents a breakthrough for the negotiations, it is unclear if it is enough of a concession to win over significant numbers of Republicans, especially House conservatives.

Also up in the air is the taxation of inherited estates, with liberals pushing for the higher level of tax that was in place a few years ago and Republicans demanding continuation of current policy.

The estate tax has emerged as a major stumbling block, sources familiar with the talks said Saturday evening. According to one person briefed on the negotiations, Reid has given Republicans a choice of lifting the income threshold above which there will be a tax increase from $250,000 to $400,000 or maintaining current estate tax provisions, which include a 35 percent tax rate and a $5.1 million exemption.

Republicans want both the higher income threshold and the lower estate tax. In addition, they want to trim a package of targeted, temporary tax breaks known as extenders and are taking particular aim at a collection of 2009 stimulus tax breaks.

Meantime, an aide to Speaker John A. Boehner, R-Ohio, confirmed he is opposed to including any delay of the sequester unless the automatic spending cuts are matched by other spending reductions.

Quiet Tension

Absent congressional action, a broad range of tax cuts enacted over the past decade will lapse at the end of the year, including reduced tax rates on ordinary income, capital gains and dividends and a 2-percentage-point drop in the Social Security payroll tax. According to the Tax Policy Center, the expiration of all tax cuts would cause federal tax collections to grow by $500 billion, or more than 20 percent, next year, with nearly 90 percent of all households facing an average increase of $3,500.

On a damp holiday weekend, Senate leadership staffers were shuttling papers between the offices of McConnell and Majority Leader Harry Reid of Nevada. Boehner made a brief visit to his office in the morning, and McConnell arrived in the building soon after Boehner left.

At least for the moment, the brightest spotlight is on McConnell, who has taken over for Boehner as the chief Republican negotiator. After a meeting at the White House Friday, congressional leaders signaled that McConnell and Reid would exchange proposals aimed at a legislative compromise that would be passed first by the Senate and then by the House.

In his weekly radio address Saturday, Obama stressed the urgency of action before the automatic tax increases take effect. “Congress can prevent it from happening if they act now,” Obama said. “Leaders in Congress are working on a way to prevent this tax hike on the middle class, and I believe we may be able to reach an agreement that can pass both houses in time.”

To satisfy the constitutional requirement that revenue measures originate in the House, the Senate would take up a House-passed tax bill (HR 8) and use it as a vehicle for a compromise that would take its place as a substitute amendment.

If a deal is not reached, Reid planned to have a vote Monday on a tax package that would conform to Obama’s preferred policies. The bill would permanently extend tax cuts on income below $250,000 for couples, index the alternative minimum tax to inflation for 2012 and prevent payment cuts to physicians and tax estates at 2009 levels, with a top rate of 45 percent and a $3.5 million exemption.

Compared with an extension of current policy, the bill would raise about $760 billion over 10 years, according to Citizens for Tax Justice, a nonprofit research group. Raising rates only on income above $400,000 or $500,000 would shave at least $100 billion from that total, and continuing to tax estates with a 35 percent top rate and a $5 million exemption would cost another $120 billion or so.

Still, Democrats might have other opportunities to add to the government’s revenue collections. Even with a cutoff above $250,000, White House officials would likely see raising rates on ordinary income, dividends and capital gains as an important step toward their goal of making the tax code more progressive.

Given the nature of the tax system, it is difficult to substantially increase the tax burden of the wealthiest households earning above $1 million without raising tax rates. But other administration proposals that would limit tax deductions and exclusions could raise significant amounts of revenue from taxpayers earning $250,000 to $1 million if the White House can advance them as part of a tax system overhaul.

Similarly, Republicans are not about to give up on their fight to cut spending. Communicating via Twitter on Friday, Rep. Justin Amash, R-Mich., said the best Republican strategy would be to quickly pass a tax cut extension for middle-income earners and then “flip [the] script” to spending in 2013.

Amash, a tea party favorite who has clashed with the GOP leadership, said he would not vote for any bill that included a spending increase. But like many Republicans, his view is that once the fight over tax rates is settled and the focus shifts to the sequester and the debt limit, Republicans will have more leverage to seek their priorities.